September 2007

High School Mathematics

Bridging innovation and tradition

Bogged down by rote-memorization drills and predictable homework exercises, EDC’s Al Cuoco was frustrated teaching math in the 1970’s. “Like many math teachers, I was always dissatisfied with most of the commercially available curricula I had.” Over the past five years, he has been working on behalf of today’s teachers “to create the texts I always yearned for.” As principal designer of a major mathematics textbook initiative, the CME Project, he says he is nearing his goal.

“While these texts have been in development for over five years,” states Cuoco, “in a real sense I’ve been working on the ideas in this program for close to four decades.”

Many high school mathematics teachers still face the dilemma that Cuoco did years ago. They must choose between traditional texts, on the one hand, that follow an accepted structure and progression—algebra, geometry, advanced algebra, and precalculus—but do not integrate lessons and themes across topics and chapters, and, on the other hand, more progressive texts that challenge students yet organize the material in a manner that is unfamiliar to teachers and parents.

“In far too many classrooms, mathematics is taught as a disconnected set of facts and procedures, a body of knowledge to be learned in much the same way as one learns a list of terms for a vocabulary test,” says Cuoco, who works in EDC’s Center for Mathematics Education.

The CME Project, funded by the National Science Foundation (NSF), features a series of textbooks focusing more on comprehension of core math concepts and less on rote memorization of facts and formulas. These new texts present mathematics in progressive and innovative ways, challenging students to develop robust mathematical proficiency. The new texts will be available in fall 2007.

Rater than forcing students to churn through chapter after chapter of disjointed topics—from graphing equations to triangle trigonometry to complex numbers—without connecting themes and ideas, CME texts present ideas thoroughly for students to get a firm handle on the material. Topics are revisited in later chapters to deepen students’ understanding of them and their connection with other ideas, while the clutter of extraneous topics is omitted.

Drawing on lessons learned from high-performing countries in the Pacific Rim and Northern Europe, the program also employs the best American models that call for “experience before formality.” This practice encourages students to grapple on their own with ideas and problems before the teacher presents the lesson in class.

The texts go beyond “real life” examples to make math interesting. Many of the tasks posed by CME are purely mathematical, such as “find the sum of integers between one and 100” and “find a simple rule that would generate the following input/output table of numbers.”

“We were surprised to discover when asking our student advisory board that they found these purely mathematical problems to be very realistic,” says Cuoco. “They didn’t need a ‘real-life’ situation or context to grasp the meaning behind the problems and apply their problem-solving skills.”

The program has drawn on the expertise of teachers, mathematicians, researchers, and students and has been extensively field tested in sites across the country—urban, suburban, and rural. The geometry and precalculus courses were field tested for their initial release, and the newer course materials have been field tested nationally for the last 2-3 years. While CME sets high expectations for students, field tests have demonstrated that these expectations can be met by students of all abilities and backgrounds.

The new texts will be published in two stages by Prentice Hall which is promoting them at the National Council of Teachers of Mathematics conference. The first collection of bound books will be released in November 2007 for adoption in 2008, starting with Algebra 1. The next two books will be published six months after that.

‘Open and Closed’

The new CME texts balance their conceptual emphasis with an ample supply of examples, formulas, and reference resources. “We wanted to develop a curriculum that is both open and closed,” states Cuoco. “Previous texts developed by EDC were very open—activities and problems designed to help students discover results for themselves with few stated theorems, definitions, or worked-out sample problems. Teachers told us they loved the open-ended presentation of material, but they wanted more closure within the student text. These new texts provide this closure, serving as a reference for students with results and examples, for instance, if they were out sick one day or simply wanted to revisit content months later.”

With CME, students start each lesson with a problem set before instruction serving as a preview—a simple numerical and geometric context—for the ideas that will follow. They then are provided worked-out examples or dialogs to explain the methods, helping to bring closure and serve as a reference for later. Students can then practice their newly developed skills and methods with practice problems. Each chapter begins with activities accessible to all students and ends with problems that will challenge the most advanced.

The CME Project builds upon an approach developed by EDC, Connected Geometry, funded by NSF in 1992. In 1999 NSF funded EDC to use similar methods and approaches to develop Mathematical Methods, a precalculus text, and in 2003 they funded the completion of the four-year program through the development of both Algebra 1 and 2 courses.

Learn more:
http://www2.edc.org/cmeproject/

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